eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2382-9761
2015-11-01
2
2
1
8
741
مقاله پژوهشی
Characterization and axiomatization of all semigroups whose square is group
M.H. Hooshmand
1
Shiraz Branch, Islamic Azad University
In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup). Finally, several equivalent conditions for a semigroup $S$ with $S^2leq S$ (the square-group property) will be considered.
http://as.yazd.ac.ir/article_741_50a5e5f483c3aa4d91f526deacc2e032.pdf
Ideal subgroup
grouplike
homogroup
class united grouplike
real grouplike
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2382-9761
2015-11-01
2
2
9
22
765
مقاله پژوهشی
When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?
S. VISWESWARAN
1
A. PARMAR
2
Saurashtra University, Rajkot
Saurashtra University, Rajkot
The rings considered in this article are commutative with identity which admit at least two nonzero annihilating ideals. Let $R$ be a ring. Let $mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $mathbb{A}(R)^{*} = mathbb{A}(R)backslash {(0)}$. The annihilating-ideal graph of $R$, denoted by $mathbb{AG}(R)$ is an undirected simple graph whose vertex set is $mathbb{A}(R)^{*}$ and distinct vertices $I, J$ are joined by an edge in this graph if and only if $IJ = (0)$. The aim of this article is to classify rings $R$ such that $(mathbb{AG}(R))^{c}$ ( that is, the complement of $mathbb{AG}(R)$) is connected and admits a cut vertex.
http://as.yazd.ac.ir/article_765_b8befa609c45c0b6b6a79bc456253b4a.pdf
N-prime of $(0)$
B-prime of $(0)$
complement of the annihilating-ideal graph of a commutative ring
vertex cut and cut vertex of a connected graph
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2382-9761
2015-11-01
2
2
23
36
784
مقاله پژوهشی
Ultra and Involution Ideals in $BCK$-algebras
Simin Saidi Goraghani
siminsaidi@yahoo.com
1
R. A. Borzooei
2
Farhangian University
Shahid Beheshti University
In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the notions of prime ideals and ultra ideals are coincide.
http://as.yazd.ac.ir/article_784_59ea8d93f1f07746b0ae002a32a6a389.pdf
$BCK$-algebra
(associative
commutative
positive implicative
implicative) ideal
ultra ideal
involution ideal
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2382-9761
2015-11-01
2
2
37
47
785
مقاله پژوهشی
The structure of a pair of nilpotent Lie algebras
Homayoon Arabyani
arabyani_h@yahoo.com
1
Hadi Hosseini Fadravi
2
Islamic Azad University
Islamic Azad University
Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpotent Lie algebras and generalize results for a pair of non-abelian nilpotent Lie algebras.
http://as.yazd.ac.ir/article_785_f8abf078bb44933f3c1b0a1d39b66275.pdf
Nilpotent Lie algebra
Pair of Lie algebras
Schur multiplier
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2382-9761
2015-11-01
2
2
49
55
803
مقاله پژوهشی
On the nil-clean matrix over a UFD
Somayeh Hadjirezaei
s.hajirezaei@vru.ac.ir
1
Somayeh Karimzadeh
2
Vali-e-Asr University of Rafsanjan
Vali-e-Asr University of Rafsanjan
In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix over a UFD is nil-clean.
http://as.yazd.ac.ir/article_803_7a98829c79d5ccc6521ac399e996e7bb.pdf
Rank of a matrix
Idempotent matrix
Nilpotent matrix
Nil-clean matrix
Strongly nil-clean matrix
eng
Yazd University
Algebraic Structures and Their Applications
2382-9761
2382-9761
2015-11-01
2
2
57
66
807
مقاله پژوهشی
$z^circ$-filters and related ideals in $C(X)$
Rostam Mohamadian
mohamadian_r@scu.ac.ir
1
Shahid Chamran University of Ahvaz
In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them with corresponding ideals, namely, $z^circ$-ideals of $C(X)$, the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter is ci-fixed. Finally, by using $z^circ$-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.
http://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf
$z^circ$-filter
prime $z^circ$-filter
ci-free $z^circ$-filter
i-free $z^circ$-filter
$z^circ$-ultrafilter
i-compact